Chapter 8.1, Problem 72PFA

To determine

To find the number of books left in the library.

Answer to Problem 72PFA

  $x^2-5x+15$

Explanation of Solution

Given:

Number of books that a library hold is $x^2-2x+10$

Number of books that Alice Checks is $3x-5$

Calculation:

Let the number of books remaining is A .

The number of books that the library hold is $x^2-2x+10.$

The number of books that is checked by Alice is $3x-5.$

The remaining number of books is the difference of the total books that the library holds and the number of books that Alice has checked.

The number of books remaining is,

  $\begin{array}{c}A=(x^2-2x+10)-(3x-5)\\ A=x^2-2x+10-3x+5\end{array}$

Combining the like terms,

  $\begin{array}{l}A=x^2-(2x+3x)+(5+10)\\ A=x^2-5x+15\end{array}$

Conclusion:

Therefore, the number of books remaining in the library is given by the expression $x^2-5x+15.$